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Omni-MATH / Altitudes BE and CF of acute triangle ABC intersect at H. Suppose that the altitudes of triangle EHF concur on line BC. If AB=3 and AC=4, then BC²=(a)/(b), where a and b are relati…

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problem

Altitudes BEB E and CFC F of acute triangle ABCA B C intersect at HH. Suppose that the altitudes of triangle EHFE H F concur on line BCB C. If AB=3A B=3 and AC=4A C=4, then BC2=abB C^{2}=\frac{a}{b}, where aa and bb are relatively prime positive integers. Compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
Altitudes BE and CF of acute triangle ABC intersect at H. Suppose that the altitudes of triangle EHF concur on line BC. If AB=3 and AC=4, then BC²=(a)/(b), where a and b are relatively prime positive integers. Compute 100a+b.
Original LaTeX notation
Altitudes $B E$ and $C F$ of acute triangle $A B C$ intersect at $H$. Suppose that the altitudes of triangle $E H F$ concur on line $B C$. If $A B=3$ and $A C=4$, then $B C^{2}=\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100 a+b$.

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Source and history

task_id
07a97e53-64b9-5618-87bb-24410732c302
task_key
test--07a97e53-64b9-5618-87bb-24410732c302
task_revision_id
1
config / split
/ test

Official source

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